A typical photovoltaic (PV) system consists of a solar array, its mounting structure, DC wiring, a battery bank (in battery-equipped systems), and an inverter. All of these components must be designed, sized, and installed correctly to work in unison to properly generate power from the sun.
Installation issues such as amount of insolation (the amount and quality of the light that reaches the array), correct array orientation, tilt, and partial shading considerations playa crucial role in the overall output of a solar system. An array that is exposed to less than the 1000 WI m2, positioned a few degrees off correct orientation, or exposed to partial shading from nearby tree limbs, power lines, or chimneys will certainly output less power than it can, but that same array is also impacted by a host of environmental conditions. The purpose of this paper is to illustrate some of the factors involved in estimating the output of a solar array.
The DC rated output of each solar module is provided by the PV manufacturer in the form of values taken under Standard Test Conditions (STC). These conditions create a specific solar environment by indicating:
- Solar Cell Temperature = 25°C (the temperature of each cell in a module)
- Solar Irradiance = 1000 W/m2 (the amount of light that shines on a module)
- ASTM Standard Spectrum (the type of light that shines on a module)
Since each module manufacturer rates the module output at STC, the system designer has the ability to compare various manufacturer’s modules and choose an array based on an "apples to apples" comparison of watts STC (for module A) vs. watts STC (for module 8). What is important to remember, is that, while STC conditions are convenient for measuring module output in a laboratory, the actual cell temperature is much lower in the laboratory than will typically be seen in the field. Since the PV output decreases with increasing temperature, this STC rating must be de-rated to arrive at a "real world" array output.
Production Tolerance - Manufacturers often assign an allowable output tolerance to the module’s rating. For example, if this tolerance is +1- 5% of the rating, a 100 watt module could actually yield 95 watts to 105 watts under STC, yet still be sold as a 100 watt device.
Temperature - The cell temperatures of a solar array will vary drastically due to ambient conditions such as sun intensity, air temperature, wind speed, and other factors. Module construction and how the array is mounted can also impact module’s cell temperature. Roof-mounted arrays typically yield peak cell temperatures in the range of 50°C to 75 °C - two to three times higher than specified by STC. To account for the higher cell temperature, a de-rating factor of 0.89 for crystalline modules has been recommended by the California Energy Commission. Thus, taking a conservative approach, a 100 watt module, factoring in production tolerances and temperature de-ratings, would essentially output only 85 watts: 100 watts (rating) x 0.95 (tolerance) x 0.89 (de-rating) = 85 watts.
Dirt and dust - Arrays mounted in real world conditions eventually become covered with a fine layer of dirt and dust, decreasing the amount of light reaching each cell. The amount power loss due to soiling depends on variables such as the location, the type of dust, and the length of time since the last rainfall. Tests performed at PVUSA in Davis, CA showed a reduced output by a factor of 0.93 while other locations have suggested as much as a 2 to 4 percent reduction. Factoring in production tolerances, temperature de-ratings, and adding a value for soiling further reduces the 100 watt module’s output to 79 watts: 100 watts (rating) x 0.95 (tolerance) x 0.89 (de-rating) x 0.93 (soiling) = 79 watts.
Mismatch and wiring losses - The sum of the whole is always less than the sum of the parts, so an array made of many modules that differ, even slightly, must be de-rated by a factor of 0.98. Furthermore, DC wiring also accounts for power losses due to the resistance of the wiring in a system. Even in a welldesigned and installed system, DC wiring losses can account for an additional de-rating factor of 0.97. Thus, the output of the 100 watt module is now down to 75 watts: 100 watts (rating) x 0.95 (tolerance) x 0.89 (de-rating) x 0.93 (soiling) x 0.98 (mismatch) x 0.97 (wiring losses) = 75 watts.
DC to AC conversion losses - We have now accounted for losses leading from a well-installed and positioned array down to the inverter. Since there are two types of grid tie inverters (without batteries and with batteries), these components must be factored into the equation as well. A system without batteries has a conversion loss (DC to AC) that is based on the inverter efficiency. On average, over a day, this efficiency is about
- 90% - resulting in a de-rating factor of 0.90 for the system without batteries. For a system with batteries, battery losses and conversion efficiency must be factored in. A battery-based system must maintain the battery at float voltage incurring additional losses. With its related components, the system with batteries has losses of about 10%. Inverter efficiency is slightly less than the system without batteries (above), averaging about 86% - resulting in a total de-rating factor of 0.77 for a system with batteries.
Environmental and equipment dynamics can have a drastic impact the output of a typical solar electric system. If the installation accounts for correct array orientation, tilt, partial shading considerations, etc., then, when calculating the output yield for a 1000 watt array, the following de-rating factors must be included:
The result, for a typical 1000 watt system, is an average 670 watts output for a system without batteries and an average 580 watts for a system with batteries - assuming a perfectly sunny day and a properly designed and installed system. This calculation accounts for environmental and equipment factors that impact system performance for demonstrative purposes only. These concepts and additional factors that impact solar electric system performance are discussed in greater detail in the "A Guide to Photovoltaic System Installation and Design" prepared by Endecon Engineering for the California Energy Commission (CEC).
- NOTE:
- "Top of Well" - also means "pitless adapter level"
- "Service Inlet" - also means "storage tank inlet"
- Standing or Static Water Level - distance from top of well to natural water level when pump is not operating.
- Drawdown Distance - standing water level plus draw down. Submergence - distance submersible pump intake screen is installed below draw down level.
- Elevation - vertical distance between top of well and service inlet.
- Pump Setting - distance from top of well to pump inlet screen
- Pumping Level - distance from draw down level to service inlet.
- Service Pressure - pressure (in PSI) at service inlet.
- Friction Loss - loss of pressure due to friction of water flowing through pipe and fittings.
- Total Discharge Head - discharge head (in feet) delivered when pump is operating at desired capacity.
- Horizontal Pipe Run - horizontal distance between service inlet and well.
- PSI - can be converted to equivalent feet of head by multiplying by 2.31.
The answer to four basic questions will help select the proper pump.
- WHAT IS THE SIZE OF THE WELL? The inside diameter of the well must be know so that the proper size pump, injector, cylinder or drop pipe and foot valve can be determined.
- WHAT IS THE PUMPING LEVEL? The vertical distance in feet from the pump to the water level while the pump is operating. If the pump is installed away from the well and is on higher ground, this elevation must also be included. Most wells draw down while being pumped so this must not be confused with the standing water level.
- WHAT SHOULD BE THE AVERAGE DISCHARGE PRESSURE? Usual average discharge pressure is 40 lbs. - halfway between the 30 lbs. to 50 lbs. switch setting of most water systems. When the tank is installed away from the pump at a higher level, or when house or yard fixtures are above the pump and tank, a greater is needed and a larger pump must be used.
- WHAT CAPACITY IS REQUIRED? The discharge capacity of the pump in gallons per hour that is needed for satisfactory service. The pump should have enough capacity so that it can deliver the total water requirement in 2 hours of continuous operation. See table of water requirements above.
AVERAGE WATER REQUIREMENTS FOR GENERAL SERVICE AROUND THE HOME AND FARM
Each person per day, for all purposes 50 gal.
Each horse, dry cow or beef animal 12 gal.
Each milking cow per day 35 gal.
Each hog per day 4 gal.
Each sheep per day 2 gal.
Each 100 chickens per day 4 gal.
AVERAGE AMOUNT OF WATER REQUIRED BY VARIOUS HOME AND YARD FIXTURES
Drinking fountains, continuous flow per day 50 to 100 gal.
Each shower bath Up to 60 gal.
To fill bathtub 30 gal.
To flush toilet 6 gal.
To fill lavatory 2 gal.
To sprinkle 1/4" of water on each 1000 square feet of lawn 160 gal.
Dish Washing machine - per load 3 gal.
Automatic Washer - per load Up to 50 gal.
Regeneration of Domestic Water Softener 50 to 100 Gal.
AVERAGE FLOW RATE REQUIREMENTS BY FIXTURE
Shower 4 to 6 GPM
Bathtub 4 to 8 GPM
Toilet 4 to 5 GPM
Lavatory 1 to 3 GPM Kitchen sink 2 to 3 GPM
1/2" hose and nozzle - per hour 200 GPH
3/4" hose and nozzle - per hour 300 GPH
Lawn sprinkler - per hour 120 GPH
MAXIMUM TOTAL HEAD is the maximum pressure that can be developed by the pump. This is always given in feet of head rather than in pounds. The pump selected must have a maximum total head greater than the sum of the PUMPING LEVEL and the TOTAL DISCHARGE HEAD.(Shown in illustration as Total Head.)
When figuring PUMPING LEVEL the following conditions must be considered:
STANDING WATER LEVEL is the distance from the top of the well to the top of the water when the pump is not operating.
DRAWDOWN is the distance the water level drops below the standing water level while the pump is operating.
ELEVATION is the distance between the ground level at the pump and the ground level at the top of the well. There is no elevation when the pump is installed right at the well.
SUBMERGENCE is the distance the injector, submersible pump, or foot valve is installed below the pumping level.
HORIZONTAL PIPE RUN is the distance the jet or piston pump is installed away from the well. (See Friction Loss.)
When figuring TOTAL DISCHARGE HEAD the following conditions must be considered:
SERVICE PRESSURE is the pressure in pounds at the point of use. (Service pressure can be converted to feet by multiplying by 2.31.)
FRICTION LOSS is the loss of pressure due to friction of water flowing through pipe and fittings. If the pump is installed some distance from the well this friction loss can be over-come by increasing the pipe size. (See page 6.)
When properly selected each of these pumps and water systems will give years of dependable satisfactory service. Never underestimate the requirements of the job. A pump a little too large will always do the job properly. A pump a little too small will either have to be replaced or will prove unsatisfactory to the owner.
FACTORS TO CONSIDER IN SELECTING PUMP FOR PUBLIC BUILDINGS
- An overhead tank should be used for systems of 250 GPM or over.
- Pneumatic systems are satisfactory for capacities below 250 GPM, but must have proper control and air compressor.
- Tankless systems should be used only in small buildings or where the pump only operates at infrequent intervals.
- Pressure on the top floor should be 15 lbs. and preferably higher.
- Where pressure tank system is used, pressure tank should be made to ASME code specifications.
- For less than 25 fixtures, pump capacity should not be less than 75% of capacity required for 25 fixtures.
- Where additional water is required for some special process, this should be added to pump capacity.
- Where laundries or swimming pools are to be supplied, add approximately 10% to pump capacity for either.
- Where the majority of occupants are women, add approximately 20% to pump capacity.
"RULE OF THUMB" formula for sizing home water systems that will be applicable in many instances:
Simply count the fixtures and water outlets in the home, and multiply by 60 gallons per hour. This method bases the approximate pumping capacity on use, at the rate of a gallon per minute per fixture, and avoids the possibility of under sizing.
For instance, let us assume you count the following list of fixtures and water outlets in your home:
Kitchen
- Sink (1)
- Dishwasher (Count as one fixture) (1)
- Lavatory (1)
- Tub (1)
- Toilet (1)
- Lavatory (1)
- Toilet (1)
- Automatic Washing Machine (Count as one fixture) (1)
- Laundry Tubs (1)
- Shower (1)
TOTAL FIXTURES AND OUTLETS (12)
12 X 60 = 720 Gallons Per Hour
Be sure that your pump installer provides a water system that will deliver 720 gallons per hour at the desired pressure.
POUNDS PRESSURE - FEET OF HEAD
Each pound of pressure developed by a pumping system is equal to 2.31 feet of head (feet of lift). Therefore, 10 pounds of pressure (PSI) will lift water vertically 23.1 feet. The chart above converts pressure to feet of head at various settings from 1 to 100 PSI.
This can be calculated for any setting using the following formula:
Head In Feet = Pounds Per Sq. In. X 2.31
FRICTION LOSS
Pipe friction is the resistance to flow created by the interior surface of the pipe through which a liquid is moving. The smaller the diameter of the pipe, or the greater the rate of flow, the greater the amount of friction (Friction Loss).
Friction Loss is expressed as feet of head in 100 feet of pipe and will vary depending upon the material of which the pipe is made. The following charts show friction losses.
Pipe size should be sufficiently large so that not more than 10% of the total dynamic head is in friction loss.
Example:
(A) 100 Ft. of 2" plastic pipe with one (1) 90 degree elbow and one (1) swing check valve.
90 degree elbow - Equivalent to 5.5 Ft. of straight pipe
Swing Check - Equivalent to 17.0 Ft. of straight pipe
100 Ft. of Pipe - Equivalent to 100.00 Ft. of straight pipe
122.5 Ft. = Total Equivalent of Pipe Figure friction loss for 122.5 Ft. of Pipe.
(B) Assume flow to be 80GPM through 2" plastic pipe.
1. Friction loss table shows 11.43 Ft. loss per 100 Ft. of Pipe.
2. In step (A) above we have determined total feet of pipe to be 122.5 Ft.
3. Covert 122.5 Ft. to percentage. 122.5 divided by 100 = 1.225.
4. Multiply 11.43 x 1.225 = 14.001 (14 Ft. = Total friction loss in this system)
TABLE FOR EQUALIZING PIPES
The size of main pipe is given in the column at the left. The number of branches is given in the line on top, and the proper size of branches is given in the body of the table on the line of each main and beneath the desired number of branches.
In commercial sizes the nominal 1 1/4" pipe is generally over-sized, often as large as 1 3/8". It is safe to call it 1.3 inch, and it is so figured in the table. Exact sizes are given for each pipes. The designer of the pipe system can thus better select the commercial sizes to be used.
ALUMINUM PIPE - FRICTION LOSS PER 100 FT.
RUBBER HOSE - FRICTION LOSS PER 100 FT.
CALCULATION OF DISCHARGE RATE USING HORIZONTAL OPEN DISCHARGE FORMULA
An L-shaped measuring square can be used to estimate flow capacity, using the chart below. As shown in the illustration, place 4" side of square so that it hangs down and touches the water. The horizontal distance shown as "A" is located in the first column of the chart and you read across to the pipe diameter (ID) to find the gallons per minute discharge rate.
Example: "A" is 8" from a 4" ID pipe = discharge rate of 166 GPM
DISCHARGE RATE IN GALLONS PER MINUTE / NOMINAL PIPE SIZE (D)
NPSH combines all the factors limiting the suction side of a pump; internal pump losses, static suction lift, friction losses, vapor pressure and atmospheric conditions. It is important to differentiate between NPSH REQUIRED and SPSH AVAILABLE.
REQUIRED NPSH is a factor designed into a pump and measurable in the test laboratory by the manufacturer.
AVAILABLE NPSH is the term for providing sufficient pressure on the pump suction, at the impeller eye, to prevent "boiling". It is a function of the pumping system and consists of; pressure on the liquid at its source, the elevation of the liquid with respect to the impeller centerline, losses in the suction piping and vapor pressure of the liquid.
If the available NPSH is not equal to, or greater than, that required by the pump, it must be increased. This may be accomplished by increasing the static head, increasing pressure on the liquid supply surface, decreasing friction loss, or decreasing liquid temperature.
NPSHA = (Barometer + Gauge - Vapor Pressure) X 2.31 divided by Specific Gravity + or - Static Height - Pipe Loss.
BAROMETER value in pounds per square inch absolute (PSIA) should be the lowest likely reading for the area where the pump will be installed. (Use table on next page, to convert barometer reading in inches of mercury to PSIA.)
GAUGE PRESSURE (PSIG) is the pressure in pounds per square inch ABOVE atmospheric pressure on the surface of the liquid in the supply vessel.
VAPOR PRESSURE is the value in pounds per square inch absolute (PSIA) at which the liquid will boil at a given temperature.
STATIC HEIGHT is the distance in feet between the pump suction centerline and the surface level of the liquid in the supply vessel. If the surface level of the liquid is higher than the pump suction, static height is positive. If the surface level of the liquid is lower than the pump suction, static height is negative.
Ft. of Water = PSI X 2.31 Divided by Specific Gravity
2) Selected pump and impeller diameter from performance curve.
3) Note pump efficiency.
4) Calculate brake horsepower required.
Break Horsepower = GPM X Head X Specific Gravity Divided by 3960 X Pump Efficiency
Specific Gravity = 141.5 Divided by 131.5 + Degrees API
To convert degrees Baume to specific gravity (liquids heavier than water)
Specific Gravity = 145 Divided by 145 - Degrees Baume
The term "Head" by itself is rather misleading. It is commonly taken to mean the difference in elevation between the suction level and the discharge level of the liquid being pumped. Although this is partially correct, it does not include all of the conditions that should be included to give an accurate description.
FRICTION HEAD
- is the pressure expressed in lbs./sq. in. of feet of liquid needed to overcome the resistance to flow in the pipe and fittings.
SUCTION LIFT- exists when the source of supply is below the center line of the pump.
SUCTION HEAD- exists when the source of supply is above the center line of the pump.
STATIC SUCTION LIFT- is the vertical distance from the center line of the pump down to the free level of the liquid source.
STATIC SUCTION HEAD- is the vertical distance from the center line of the pump up to the free level of the liquid source.
STATIC DISCHARGE HEAD- is the vertical elevation from the center line of the pump to the point of free discharge.
DYNAMIC SUCTION LIFT- includes static suction lift, friction head loss, and velocity head.
DYNAMIC SUCTION HEAD- includes static suction head minus friction head minus velocity head.
DYNAMIC DISCHARGE HEAD- includes static discharge head plus friction head plus velocity head.
TOTAL DYNAMIC HEAD- includes the dynamic discharge head plus dynamic suction lift or minus dynamic suction head.
VELOCITY HEAD- is the head needed to accelerate the liquid. Knowing the velocity of the liquid, the velocity head loss can be calculated by a simple formula,
Head = V squared divided by 2 x g in which g is acceleration due to gravity or 32.16 Ft./sec squared.
Direct ratio of any liquid’s weight to the weight of water at 62 degrees F. Water at 62 degrees F. weighs 8.33 lbs. per gallon and is designated 1.0 Specific Gravity.
Note: A centrifugal pump develops head, not pressure. All pressure figures should be converted to feet of head taking into consideration the Specific Gravity (Ft. HD = PSI X 2.31 - Sp. Gr.)
VISCOSITYProperty of all liquid that resists any force tending to flow. It is the evidence of cohesion between the particles of a fluid which causes a liquid to offer resistance analogous to friction. An increase in the temperature usually reduces the viscosity; conversely, a temperature reduction usually increases the viscosity. Pipe friction loss increases as viscosity increases.
EFFECTS OF VISCOSITYViscous liquids tend to increase pump head, reduce efficiency, reduce capacity, head and increase pip friction.
A centrifugal pump will produce less capacity and less head as pump rpm is reduced or as impeller diameter is reduced. Generally speaking, the changes caused by changing the impeller diameter must be determined by test. It is impractical to attempt to estimate new duties by changing impeller diameters without the use of laboratory test data.
When pumping rpm is changed, however, new duties may be calculated with useable accuracy. This is accomplished by using factors called "affinity laws". Simply stated, the affinity laws state that,
1.) pump capacity changes directly with speed change.2.) head changes with the square of the pumping rpm.
3.) brake horsepower changes with the cube of pumping rpm.
In formula form:
In short, if the pumping rpm were doubled,
1.) the capacity would double
2.) the head would be multiplied 4 times
3.) the brake horsepower would be multiplied by 8
The efficiency would not change.
Conversely, if the pump rpm were cut in half,
1.) the pump capacity would be divided by 2
2.) the head would be divided by 4
3.) the horsepower would be divided by 8
Generally speaking, cutting impeller diameters alters pump efficiency. This is the reason why affinity laws cannot be effectively applied to changes in pump performance when impeller diameter is altered.
Cavitation is a term used to describe a rather complex phenomenon that may exist in a pumping installation. In a centrifugal pump this may be explained as follows. When a liquid flows through the suction line and enters the eye of the pump impeller an increase in velocity takes place. This increase in velocity is, of course, accompanied by a reduction in pressure. If the pressure falls below the vapor pressure corresponding to the temperature of the liquid, the liquid will vaporize and the flowing stream will consist of liquid plus pockets of vapor. Flowing further through the impeller, the liquid reaches a region of higher pressure and the cavities of vapor collapse. It is this collapse of vapor pockets that causes the noise incident to cavitation.
Cavitation need not be a problem in a pump installation if the pump is properly designed and installed, and operated in accordance with the designer’s recommendations. Also, cavitation is not necessarily destructive. Cavatation varies from very mild to very server. A pump can operate rather noiselessly yet be cavitating mildly. The only effect may be a slight drop in efficiency. On the other hand severe cavitation will be very noisy and will destroy the pump impeller and/or other parts of the pump.
Any pump can be made to cavitate, so care should be taken in selecting the pump and planning the installation. For centrifugal pumps avoid as much as possible the following conditions:
1. Heads much lower than head at peak efficiency of pump.2. Capacity much higher than capacity at peak efficiency of pump.
3. Suction lift higher of positive head lower than recommended by manufacturer.
4. Liquid temperatures higher than that for which the system was originally designed.
5. Speeds higher than manufacturer’s recommendation.
Cavitation is not confined to pumping equipment alone. It also occurs in piping systems where the liquid velocity is high and the pressure is low. Cavitation should be suspected when noise is heard in pipe lines at sudden enlargements of the pipe cross-section, sharp bends, throttled valves or like situations.
FLOW OF WATER DUE TO GRAVITY OR TANK PRESSURETo determine the approximate flow in GPM through a given pipe due to gravity refer to friction tables. First determine vertical distance in feet from point of inlet to the lower point of discharge. Multiply the figure by 100 and divide by length of pipe line in feet. Use the result of above and locate this number of feet on the appropriate pipe size chart and type column.
Read directly across to the left from this pint to determine GPM that will flow through pipe.
FOR PRESSURE TANKS - Convert pounds of pressure to feet head. (20psi x 2.31 = 46.1 Ft.) 20 pounds will flow as much water as gravity tank with elevation of 46.1 Ft.
Flow of water at end of pipe will be at zero pressure.
Install sufficient 1/8" or 1/4" piping (copper tubing may also be used) in the well so that end of pipe extends 10 to 20 feet below lowest possible pumping level. Be sure that all joints are absolutely air-tight by using white-lead or pipe compound.THE EXACT LENGTH OF PIPE OR TUBING IN THE WELL MUST BE KNOWN AND THIS INFORMATION SHOULD BE RECORDED.
Attach upper end of pipe or tubing securely at top of well. Connect a tire valve to the air line at the top of the well and also a pressure gauge. Next connect a tire pump or other air supply to the air line and pump air into the line until the pressure gauge reaches a maximum reading. This reading is the point at which further supply of air will not increase the reading to any higher value. Record the gauge reading.
Let...X = Depth to water (in feet) unknown
Y = Known length of air line (in feet)
Z = Water pressure on air line, obtained from pressure gauge reading.
Altitude type gauge reads directly in feet of water. If gauge reads in pounds, convert to feet by multiplying by 2.31.
X = Y-Z
Distance to water = length of air line minus gauge reading (feet).
